Max-Plus Algebra >> Max-Plus Algebra > maxplusdelay

maxplusdelay

Max-plus algebra delay

Calling Sequence

[z] = maxplusdelay(x,d,T,A)

Parameters

x: : vector of real departure, may contain some delays
d: : vector of initial timetable
T: : timetable period, usually bigger than eigenvalue of A
A: : square input matrix
z: : matrix of delays

Description

This function returns z, the matrix that contains propagation of delays until the delay is gone.

The model of the system is given by

x(k+1)=A⊗x(k)⊕d(k+), x(0)=x,

where d(k) is the schedulling vector. The timetable d(k) is realistic if for all k≥0

A⊗d(k)≤d(k+1).

For detail see: J.G. Braker, "Algorithms and Applications Timed Discrete Event Systems”, Ph.D thesis, Department of Technical Mathematics an Informatics Delft University of Technology, (1993).

Examples

A  = [2.       7.  -%inf    7.    2.;
      -%inf  -%inf    9.    2. -%inf;
      8.       6.     1.    5. -%inf;
      0.       8.     6.    2.    2.;
      3.       7.     7. -%inf -%inf];

[lam,vx] = maxplusmaxalgol(A)
vx  =

   40.
   41.
   40.
   41.
   40.
lam  =

   8.

d = [0;0;0;0;0];
x = [7;7;7;7;7];
T = 10;
z = maxplusdelay(x,d,T,A)
z  =

   7.    4.    3.    1.    0.
   7.    6.    4.    1.    0.
   7.    5.    2.    1.    0.
   7.    5.    4.    2.    0.
   7.    4.    3.    1.    0. 

// This means that after k=4 the delay will be gone.

Author

Subiono